Rings and Fields provides an accessible introduction to rings and fields that will give the reader an appreciation of the power of algebraic techniques to handle diverse and difficult problems. A review of the prerequisite mathematics is given at the start of the book. Dr Ellis presents his ideas clearly and practically. Rather than presenting theory in abstract terms, chapters begin by introducing a problem and then go on to develop the necessary algebraic techniques for its solution in a purposeful, lucid manner, using concrete mathematical and non-mathematical examples. Although prior knowledge of group theory is unnecessary to understand the rest of the book, for those interested there is a chapter which states the axiom for a group and proves the group theoretic results needed in Galois theory.
'Clearly, this book is not meant to compete with comprehensive and systematic expositions of algebra. However, the mixture of applications and theory provides an interesting supplement.'
Mathematics Abstracts, 773/93
Preliminaries; Diophantine equations: Euclidean domains; Construction of projective planes: splitting fields and finite fields; Error codes: primitive elements and subfields; Construction of primitive polynomials: cyclotomic polynomials and factorization; Rule and compass constructions: irreducibility and constructibility; Pappus' theorem and Desargues' theorem in projective planes: Wedderburn's theorem; Solution of polynomials by radicals: Galois
groups; Introduction to groups; Cryptography: elliptic curves and factorization; Further reading; Index.